Finite Group Databasebeta

← #34305641

Subgroups — #34305641

Order 20224.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23771917C211yesmaximal, characteristic
2#23771846C211yesmaximal, characteristic
3#23764110C211yesmaximal, characteristic, complemented
4#23764103C211yesmaximal, characteristic, complemented
5#23764048C211yesmaximal, characteristic, complemented
6#23764048C211yesmaximal, characteristic, complemented
7#23763674C211yesmaximal, characteristic, complemented
8#23763674C211yesmaximal, characteristic, complemented
9#23763499C211yesmaximal, characteristic, complemented
10#23763440C211yesmaximal, characteristic, complemented
11#23763343C211yesmaximal, characteristic
12#23763246C211yesmaximal, characteristic, complemented
13#23763239C211yesmaximal, characteristic, complemented
14#23763186C211yesmaximal, characteristic, complemented
15C79×#2924C211yesmaximal, characteristic, complemented
16C22×#11929624C2211yescharacteristic
17C2×#14579167C2211yescharacteristic
18C2×#14579167C2211yescharacteristic
19C22×#11929608C2211yescharacteristic
20C2×#14579096C2211yescharacteristic, complemented
21C2×#14579096C2211yescharacteristic, complemented
22C2×#14579087C2211yescharacteristic
23C2×#14579087C2211yescharacteristic
24C2×#14579087C2211yescharacteristic
25C2×#14579087C2211yescharacteristic
26#19098571C411yescharacteristic, complemented
27#19098571C411yescharacteristic, complemented
28#19098567C411yescharacteristic, complemented
29#19098567C411yescharacteristic, complemented
30#19098562C411yescharacteristic, complemented
31#19098562C411yescharacteristic, complemented
32#19098562C411yescharacteristic, complemented
33#19098562C411yescharacteristic, complemented
34#19098557C2211yescharacteristic
35#19098557C2211yescharacteristic
36#19098557C2211yescharacteristic
37#19098557C2211yescharacteristic
38#19098529C2211yescharacteristic
39#19098529C2211yescharacteristic
40#19098528—21no—
41#19098528—21no—
42#19098527C2211yescharacteristic
43#19098525—21no—
44C22⋊C8×D79—21no—
45C2×#14579071C2211yescharacteristic, complemented
46C2×C8×Dic79C2211yescharacteristic, complemented
47C4×C22⋊Dic79C2211yescharacteristic
48#19098327C2211yescharacteristic, complemented
49#19098327C2211yescharacteristic, complemented
50#19098322C2211yescharacteristic, complemented
51#19098322C2211yescharacteristic, complemented
52#19098322C2211yescharacteristic, complemented
53#19098322C2211yescharacteristic, complemented
54#19098317C2211yescharacteristic, complemented
55#19098317C2211yescharacteristic, complemented
56C2×#117×C79C2211yescharacteristic
57#433×C79—21no—
58#433×C79—21no—
59#432×C79—21no—
60#431×C79—21no—
61#424×C79C2211yescharacteristic, complemented
62#424×C79C2211yescharacteristic, complemented
63#407×C79C2211yescharacteristic
64C2×C22⋊C8×C79C2211yescharacteristic
65#405×C79C2211yescharacteristic, complemented
66#405×C79C2211yescharacteristic, complemented
67C2×#11929624—21no—
68C2×#11929624—21no—
69C2×#11929624—22no—
70C2×#11929624—22no—
71C2×#11929624—41no—
72C2×#11929624—41no—
73C2×#11929624C2×C411yescharacteristic
74C2×#11929624C2×C411yescharacteristic
75C2×#11929624C2311yescharacteristic
76C2×#11929624C2311yescharacteristic
77C22×Dic158C2×C411yescharacteristic
78C22×D316C2×C411yescharacteristic
79C22×C22⋊D79—21no—
80C22×C4×D79—21no—
81#14579167—22no—
82#14579167—22no—
83#14579167—41no—
84#14579167—41no—
85C2×#11929608—41no—
86C2×#11929608—41no—
87C2×#11929608C2×C411yescharacteristic
88C2×#11929608C2×C411yescharacteristic
89C2×#11929608C2×C411yescharacteristic
90C2×#11929608C2×C411yescharacteristic
91C2×#11929608C2311yescharacteristic
92C2×#11929608C2311yescharacteristic
93C2×#11929607—21no—
94C2×#11929607—21no—
95C22×C79⋊C8C2311yescharacteristic
96C22×C79⋊C8C2311yescharacteristic
97C2×C8×D79—21no—
98C2×C8×D79—21no—
99C2×C22⋊Dic79—21no—
100C2×C4×Dic79C2311yescharacteristic
101C2×C4×Dic79C2311yescharacteristic
102#14579096—41no—
103#14579096—41no—
104#14579087—22no—
105#14579087—22no—
106#14579087—41no—
107#14579087—41no—
108#14579084C2×C411yescharacteristic
109#14579084C2×C411yescharacteristic
110#14579084C2×C411yescharacteristic
111#14579084C2×C411yescharacteristic
112#14579084C2×C411yescharacteristic
113#14579084C2×C411yescharacteristic
114#14579084C2×C411yescharacteristic
115#14579084C2×C411yescharacteristic
116#14579081C2×C411yescharacteristic
117#14579081C2×C411yescharacteristic
118#14579081C2×C411yescharacteristic
119#14579081C2×C411yescharacteristic
120#14579081C2×C411yescharacteristic
121#14579081C2×C411yescharacteristic
122#14579081C2×C411yescharacteristic
123#14579081C2×C411yescharacteristic
124C22⋊(C79⋊C8)—21no—
125C22⋊(C79⋊C8)—21no—
126(C2×D79)⋊C8—21no—
127(C2×D79)⋊C8—21no—
128(C2×D79)⋊C8—21no—
129(C2×D79)⋊C8—21no—
130#14579071—41no—
131C8×Dic79—41no—
132C79⋊#95—21no—
133C23×C4×C79C2311yescharacteristic
134C2×M16×C79C2311yescharacteristic
135C2×M16×C79C2311yescharacteristic
136C22×C8×C79C2311yescharacteristic
137C22×C8×C79C2311yescharacteristic
138#117×C79—21no—
139#117×C79—21no—
140#117×C79C2×C411yescharacteristic
141#117×C79C2×C411yescharacteristic
142#117×C79C2311yescharacteristic
143#117×C79C2311yescharacteristic
144C2×C4⋊C4×C79C2×C411yescharacteristic
145C2×C4⋊C4×C79C2×C411yescharacteristic
146C2×C22⋊C4×C79—21no—
147C2×C42×C79—21no—
148C4⋊C8×C79—21no—
149C4⋊C8×C79—21no—
150C4⋊C8×C79—21no—
151C4⋊C8×C79—21no—
152C22⋊C8×C79—21no—
153C22⋊C8×C79—21no—
154C22⋊C8×C79D411yescharacteristic
155C22⋊C8×C79D411yescharacteristic
156C22⋊C8×C79D411yescharacteristic
157C22⋊C8×C79D411yescharacteristic
158#97×C79—21no—
159#97×C79—21no—
160C4×C8×C79—21no—
161C4×C8×C79—21no—
162C23×D79—21no—
163#11929624—21no—
164#11929624—21no—
165#11929624—22no—
166#11929624—22no—
167#11929624—21no—
168#11929624—21no—
169#11929624—21no—
170#11929624—21no—
171#11929624—42no—
172#11929624—42no—
173#11929624—41no—
174#11929624—41no—
175#11929624—42no—
176#11929624—42no—
177#11929624#4112yes—
178#11929624#4112yes—
179C2×Dic158—22no—
180C2×Dic158—21no—
181C2×Dic158—41no—
182C2×Dic158C22×C411yescharacteristic
183C2×Dic158C22×C411yescharacteristic
184C2×D316—22no—
185C2×D316—21no—
186C2×D316—41no—
187C2×D316C22×C411yescharacteristic
188C2×D316C22×C411yescharacteristic
189C2×C22⋊D79—21no—
190C2×C22⋊D79—21no—
191C2×C22⋊D79—21no—
192C2×C22⋊D79—21no—
193C2×C22⋊D79—42no—
194C2×C22⋊D79—42no—
195C22×Dic79—21no—
196C22×Dic79—21no—
197C22×Dic79—21no—
198C2×C4×D79—21no—
199C2×C4×D79—21no—
200C2×C4×D79—21no—
201C2×C4×D79—21no—
202C2×C4×D79—42no—
203C2×C4×D79—42no—
204#11929608—21no—
205#11929608—21no—
206#11929608—21no—
207#11929608—21no—
208#11929608—41no—
209#11929608—41no—
210#11929608—41no—
211#11929608—41no—
212#11929607—42no—
213#11929607—42no—
214C2×C79⋊C8—21no—
215C2×C79⋊C8—21no—
216C2×C79⋊C8—21no—
217C2×C79⋊C8—21no—
218C2×C79⋊C8—21no—
219C2×C79⋊C8—21no—
220C2×C79⋊C8C22×C411yescharacteristic
221C2×C79⋊C8C22×C411yescharacteristic
222C2×C79⋊C8C22×C411yescharacteristic
223C2×C79⋊C8C22×C411yescharacteristic
224C8×D79—42no—
225C8×D79—42no—
226C22⋊Dic79—42no—
227C4×Dic79—21no—
228C4×Dic79—21no—
229C4×Dic79—21no—
230C4×Dic79—21no—
231C24×C79#4111yescharacteristic
232C22×C4×C79—21no—
233C22×C4×C79—21no—
234C22×C4×C79—21no—
235C22×C4×C79—21no—
236C22×C4×C79—21no—
237C22×C4×C79—21no—
238C22×C4×C79C22×C411yescharacteristic
239C22×C4×C79C22×C411yescharacteristic
240C22×C4×C79C2×D411yescharacteristic
241C22×C4×C79C2×D411yescharacteristic
242C22×C4×C79#4111yescharacteristic
243C22×C4×C79C2411yescharacteristic
244M16×C79—21no—
245M16×C79—21no—
246M16×C79—21no—
247M16×C79—21no—
248C2×C8×C79—21no—
249C2×C8×C79—21no—
250C2×C8×C79—21no—
251C2×C8×C79—21no—
252C2×C8×C79—21no—
253C2×C8×C79—21no—
254C2×C8×C79C2×D411yescharacteristic
255C2×C8×C79C2×D411yescharacteristic
256C2×C8×C79C2×D411yescharacteristic
257C2×C8×C79C2×D411yescharacteristic
258C4⋊C4×C79—21no—
259C4⋊C4×C79—21no—
260C4⋊C4×C79C22×C411yescharacteristic
261C4⋊C4×C79C22×C411yescharacteristic
262C4⋊C4×C79C22×C411yescharacteristic
263C4⋊C4×C79C22×C411yescharacteristic
264C22⋊C4×C79—21no—
265C22⋊C4×C79—21no—
266C22⋊C4×C79—21no—
267C22⋊C4×C79—21no—
268C42×C79—21no—
269C42×C79—21no—
270C42×C79—21no—
271C42×C79—21no—
272C23×C79—21no—
273C23×C79—21no—
274C23×C79—41no—
275C23×C79—41no—
276C23×C79C4×D411yescharacteristic
277C23×C79C4×D411yescharacteristic
278C23×C79C2×#4111yescharacteristic
279C22×D79—21no—
280C22×D79—21no—
281C22×D79—42no—
282C22×D79—42no—
283C22×D79—81no—
284C2×C4×C79—21no—
285C2×C4×C79—21no—
286C2×C4×C79—21no—
287C2×C4×C79—21no—
288C2×C4×C79—21no—
289C2×C4×C79—21no—
290C2×C4×C79—21no—
291C2×C4×C79—21no—
292C2×C4×C79—21no—
293C2×C4×C79—21no—
294C2×C4×C79—21no—
295C2×C4×C79—21no—
296C2×C4×C79—21no—
297C2×C4×C79—21no—
298C2×C4×C79—42no—
299C2×C4×C79—81no—
300C2×C4×C79C4×D411yescharacteristic
301C2×C4×C79C4×D411yescharacteristic
302C2×C4×C79C23×C411yescharacteristic
303C2×C4×C79C22×D411yescharacteristic
304C2×C4×C79C2×#4111yescharacteristic
305C2×C4×C79C2×#4111yescharacteristic
306C2×C4×C79H(5,𝔽2)11yescharacteristic
307C2×C4×C79H(5,𝔽2)11yescharacteristic
308C22⋊D79—22no—
309C22⋊D79—22no—
310C22⋊D79—42no—
311C22⋊D79—42no—
312C22⋊D79—41no—
313C22⋊D79—41no—
314C2×Dic79—21no—
315C2×Dic79—22no—
316C2×Dic79—21no—
317C2×Dic79—42no—
318C2×Dic79—41no—
319C2×Dic79—41no—
320C2×Dic79—41no—
321C2×Dic79—41no—
322C2×Dic79—41no—
323D316—21no—
324D316—21no—
325D316—21no—
326D316—42no—
327D316#11712yes—
328C4×D79—22no—
329C4×D79—22no—
330C4×D79—42no—
331C4×D79—42no—
332C4×D79—41no—
333C4×D79—41no—
334Dic158—21no—
335Dic158—21no—
336Dic158—21no—
337Dic158—42no—
338Dic158#11712yes—
339C8×C79—21no—
340C8×C79—21no—
341C8×C79—21no—
342C8×C79—21no—
343C8×C79—41no—
344C8×C79—41no—
345C79⋊C8—21no—
346C79⋊C8—21no—
347C79⋊C8—21no—
348C79⋊C8—21no—
349C79⋊C8—41no—
350C79⋊C8—41no—
351C22×C79—21no—
352C22×C79—21no—
353C22×C79—21no—
354C22×C79—21no—
355C22×C79—21no—
356C22×C79—21no—
357C22×C79—21no—
358C22×C79—21no—
359C22×C79—81no—
360C22×C79—81no—
361C22×C79C2×C4×D411yescharacteristic
362C22×C79#55111yescharacteristic
363C22×C79#55111yescharacteristic
364C2×D79—22no—
365C2×D79—41no—
366C2×D79—41no—
367C2×D79—41no—
368C2×D79—41no—
369C2×D79—41no—
370C2×D79—84no—
371C4×C79—21no—
372C4×C79—21no—
373C4×C79—41no—
374C4×C79—41no—
375C4×C79—41no—
376C4×C79—41no—
377C4×C79C2×#11711yescharacteristic
378C4×C79#51811yescharacteristic
379C4×C79#54611yescharacteristic
380C4×C79#54611yescharacteristic
381Dic79—22no—
382Dic79—42no—
383Dic79—41no—
384Dic79—81no—
385#22588—791nomaximal, Sylow
386C2×C79—21no—
387C2×C79—21no—
388C2×C79—41no—
389C2×C79—41no—
390C2×C79#234211yescharacteristic
391C2×C79#295511yescharacteristic
392C2×C79#295611yescharacteristic
393D79—42no—
394D79—81no—
395#2924D7911yescharacteristic, complemented
396#2896—791no—
397#2880—791no—
398#1938—791no—
399#1937—791no—
400#1929—791no—
401#1929—791no—
402#1866—791no—
403#1866—791no—
404#1826—791no—
405#1811—791no—
406#1789—791no—
407#1765—791no—
408#1764—791no—
409#1753—791no—
410C79#2258811yescharacteristic, complemented, Sylow
411C22×#41—791no—
412C2×#131—791no—
413C2×#131—791no—
414C22×M16—791no—
415C2×#117C2×D7911yescharacteristic
416#433—21no—
417#433—21no—
418#432—21no—
419#431—21no—
420C2×#108—791no—
421C2×#108—791no—
422#424C2×D7911yescharacteristic, complemented
423#424C2×D7911yescharacteristic, complemented
424C2×#104—791no—
425C2×#104—791no—
426C2×#104—791no—
427C2×#104—791no—
428#419—791no—
429#419—791no—
430#418—791no—
431#418—791no—
432#417—791no—
433#417—791no—
434#417—791no—
435#417—791no—
436#416—791no—
437#416—791no—
438#416—791no—
439#416—791no—
440#408—791no—
441#408—791no—
442#408—1581no—
443#408—1581no—
444#407—791no—
445#407—1581no—
446#407C2×D7911yescharacteristic
447C2×C22⋊C8—1581no—
448C2×C22⋊C8C2×D7911yescharacteristic
449#405C2×D7911yescharacteristic, complemented
450#405C2×D7911yescharacteristic, complemented
451C2×#97—791no—
452C2×C4×C8—791no—
453C4×C22⋊C4—791no—
454#341—791no—
455#341—791no—
456#339—791no—
457#339—791no—
458#339—791no—
459#339—791no—
460#336—791no—
461#336—791no—
462C2×#41—3161no—
463C2×#41—3161no—
464C2×#41—791no—
465C2×#41—791no—
466C2×#41—791no—
467C2×#41—791no—
468C2×#41—1582no—
469C2×#41—1582no—
470C2×#41—1581no—
471C2×#41—1581no—
472C22×Q8—791no—
473C22×D4—791no—
474C22×D4—1581no—
475C23×C4—1581no—
476C23×C4C22×D7911yescharacteristic
477#131—3161no—
478#131—3161no—
479#131—1582no—
480#131—1582no—
481C2×M16—3161no—
482C2×M16—3161no—
483C2×M16—791no—
484C2×M16—791no—
485C2×M16—791no—
486C2×M16—791no—
487C2×M16—791no—
488C2×M16—791no—
489C2×M16—1581no—
490C2×M16—1581no—
491C2×M16C22×D7911yescharacteristic
492C2×M16C22×D7911yescharacteristic
493C22×C8—791no—
494C22×C8—791no—
495C22×C8—1581no—
496C22×C8—1581no—
497C22×C8C22×D7911yescharacteristic
498C22×C8C22×D7911yescharacteristic
499#117—21no—
500#117—21no—
501#117C4×D7911yescharacteristic
502#117C4×D7911yescharacteristic
503#117C22×D7911yescharacteristic
504#117C22×D7911yescharacteristic
505C2×C4⋊C4C4×D7911yescharacteristic
506C2×C4⋊C4C4×D7911yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—1581no—
509C2×C42—21no—
510C2×C42—791no—
511C2×C42—791no—
512#108—3161no—
513#108—3161no—
514C4⋊C8—21no—
515C4⋊C8—21no—
516C4⋊C8—21no—
517C4⋊C8—21no—
518#104—3161no—
519#104—3161no—
520#104—1582no—
521#104—1582no—
522#103—791no—
523#103—791no—
524#103—791no—
525#103—791no—
526#103—791no—
527#103—791no—
528#103—791no—
529#103—791no—
530#102—791no—
531#102—791no—
532#102—791no—
533#102—791no—
534#102—791no—
535#102—791no—
536#102—791no—
537#102—791no—
538C22⋊C8—21no—
539C22⋊C8—21no—
540C22⋊C8—1581no—
541C22⋊C8—1581no—
542C22⋊C8—1581no—
543C22⋊C8—1581no—
544C22⋊C8—1581no—
545C22⋊C8—1581no—
546C22⋊C8C22⋊D7911yescharacteristic
547C22⋊C8C22⋊D7911yescharacteristic
548C22⋊C8C22⋊D7911yescharacteristic
549C22⋊C8C22⋊D7911yescharacteristic
550#97—21no—
551#97—21no—
552#97—3161no—
553C4×C8—21no—
554C4×C8—21no—
555C4×C8—3161no—
556#95—1581no—
557C24—1581no—
558C24#1192962411yescharacteristic
559#41—3162no—
560#41—3162no—
561#41—3161no—
562#41—3161no—
563#41—3162no—
564#41—3162no—
565#41—792no—
566#41—792no—
567#41—1582no—
568#41—1582no—
569#41—1581no—
570#41—1581no—
571#41—1581no—
572#41—1581no—
573#41—1581no—
574#41—1581no—
575C2×Q8—3161no—
576C2×Q8—791no—
577C2×Q8—791no—
578C2×Q8—1582no—
579C2×Q8—1581no—
580C2×D4—3161no—
581C2×D4—3162no—
582C2×D4—3162no—
583C2×D4—791no—
584C2×D4—791no—
585C2×D4—1582no—
586C2×D4—1581no—
587C2×D4—1581no—
588C2×D4—1581no—
589C2×D4—1581no—
590C2×D4—1581no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—3162no—
598C22×C4—3162no—
599C22×C4—1581no—
600C22×C4—1581no—
601C22×C4—1581no—
602C22×C4—1581no—
603C22×C4—1581no—
604C22×C4—1581no—
605C22×C4—1581no—
606C22×C4C2×C4×D7911yescharacteristic
607C22×C4C2×C4×D7911yescharacteristic
608C22×C4C2×C22⋊D7911yescharacteristic
609C22×C4C2×C22⋊D7911yescharacteristic
610C22×C4#1192962411yescharacteristic
611C22×C4C23×D7911yescharacteristic
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—3162no—
617M16—3162no—
618M16—3161no—
619M16—3161no—
620M16—3161no—
621M16—3161no—
622M16—1581no—
623M16—1581no—
624M16—1581no—
625M16—1581no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—3162no—
633C2×C8—3162no—
634C2×C8—791no—
635C2×C8—791no—
636C2×C8—791no—
637C2×C8—791no—
638C2×C8—1581no—
639C2×C8—1581no—
640C2×C8—1581no—
641C2×C8—1581no—
642C2×C8—1581no—
643C2×C8—1581no—
644C2×C8C2×C22⋊D7911yescharacteristic
645C2×C8C2×C22⋊D7911yescharacteristic
646C2×C8C2×C22⋊D7911yescharacteristic
647C2×C8C2×C22⋊D7911yescharacteristic
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4C2×C4×D7911yescharacteristic
651C4⋊C4C2×C4×D7911yescharacteristic
652C4⋊C4C2×C4×D7911yescharacteristic
653C4⋊C4C2×C4×D7911yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—3162no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—1581no—
664C42—1581no—
665C42—1581no—
666C42—1581no—
667C23—21no—
668C23—21no—
669C23—41no—
670C23—41no—
671C23—3162no—
672C23—3162no—
673C23—6321no—
674C23—1581no—
675C23—1581no—
676C23C4×C22⋊D7911yescharacteristic
677C23C4×C22⋊D7911yescharacteristic
678C23C2×#1192962411yescharacteristic
679Q8—3162no—
680Q8—792no—
681Q8—1581no—
682Q8—1581no—
683Q8—1581no—
684D4—3162no—
685D4—3162no—
686D4—3161no—
687D4—3161no—
688D4—3162no—
689D4—792no—
690D4—1582no—
691D4—1582no—
692D4—1581no—
693D4—1581no—
694D4—1581no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—42no—
710C2×C4—81no—
711C2×C4—3162no—
712C2×C4—3162no—
713C2×C4—3161no—
714C2×C4—3161no—
715C2×C4—3162no—
716C2×C4—3161no—
717C2×C4—3161no—
718C2×C4—3161no—
719C2×C4—3161no—
720C2×C4—3161no—
721C2×C4—1582no—
722C2×C4—1581no—
723C2×C4—1581no—
724C2×C4—1582no—
725C2×C4—1582no—
726C2×C4C4×C22⋊D7911yescharacteristic
727C2×C4C4×C22⋊D7911yescharacteristic
728C2×C4C22×C4×D7911yescharacteristic
729C2×C4C22×C22⋊D7911yescharacteristic
730C2×C4#41×D7911yescharacteristic
731C2×C4#41×D7911yescharacteristic
732C2×C4#1457920711yescharacteristic
733C2×C4#1457920711yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—41no—
739C8—41no—
740C8—3161no—
741C8—3161no—
742C8—1581no—
743C8—1581no—
744C8—1581no—
745C8—1581no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—81no—
755C22—81no—
756C22—3161no—
757C22—3161no—
758C22—3161no—
759C22—3161no—
760C22—3161no—
761C22—6324no—
762C22—1582no—
763C22C2×C4×C22⋊D7911yescharacteristic
764C22#1909923711yescharacteristic
765C22#1909923711yescharacteristic
766C4—21no—
767C4—21no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—3162no—
773C4—3161no—
774C4—6321no—
775C4—1582no—
776C4#117×D7911yescharacteristic
777C4#1909903711yescharacteristic
778C4#1909920111yescharacteristic
779C4#1909920111yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—3162no—
785C2—6321no—
786C2#2376625011yescharacteristic
787C2#2377230111yescharacteristic
788C2#2377230711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#2924C2
socleC22×C79C2×C4×D4
prime radicalC22×#11929624C22
cosocleC22×C4×C79C24
hypercenter#2924D79
hypocenterC79#22588
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2924

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #23764110C2semidirect
4. #23764103C2semidirect
5. #23764048C2semidirect
6. #23764048C2semidirect
7. #23763674C2semidirect
8. #23763674C2semidirect
9. #23763499C2semidirect
10. #23763440C2semidirect
12. #23763246C2semidirect
13. #23763239C2semidirect
14. #23763186C2semidirect
15. C79×#2924C2semidirect
20. C2×#14579096C22semidirect
21. C2×#14579096C22semidirect
26. #19098571C4semidirect
27. #19098571C4semidirect
28. #19098567C4semidirect
29. #19098567C4semidirect
30. #19098562C4semidirect
31. #19098562C4semidirect
32. #19098562C4semidirect
33. #19098562C4semidirect
45. C2×#14579071C22semidirect
46. C2×C8×Dic79C22semidirect
48. #19098327C22semidirect
49. #19098327C22semidirect
50. #19098322C22semidirect
51. #19098322C22semidirect
52. #19098322C22semidirect
53. #19098322C22semidirect
54. #19098317C22semidirect
55. #19098317C22semidirect
61. #424×C79C22semidirect
62. #424×C79C22semidirect
65. #405×C79C22semidirect
66. #405×C79C22semidirect
395. #2924D79semidirect
410. C79#22588semidirect
422. #424C2×D79semidirect
423. #424C2×D79semidirect
449. #405C2×D79semidirect
450. #405C2×D79semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237719172
#237718462
#237641102
#237641032
#237640482
#237636742
#237634992
#237634402
#237633432
#237632462
#237632392
#237631862
C79×#29242
#2258879